Slides: https://www.andreashandel.com/presentations/
2025-04-25
Virus load for different infections.
\[ \begin{aligned} \textrm{Uninfected cells} \qquad \dot{U} & = - bUV \\ \textrm{Infected cells} \qquad \dot{I} & = bUV - d_I I - k_M M I - k_T T I\\ \textrm{Virus} \qquad \dot{V} & = pI - d_V V \\ \textrm{Macrophages} \qquad \dot{F} & = (s + g_V)(M^* - M - \alpha k_M M I) - d_M M \\ \textrm{T cells} \qquad \dot{T} & = \frac{r_T T V}{V + h_V} - d_T T \\ \end{aligned} \]
With the right types of immune response terms in the models, one can capture patterns seen in the data.
Example of BioNTech/Pfizer COVID Vaccine
Claim: Knowing in more detail how dose impacts host response following vaccination might help optimize vaccines.
\[ \begin{aligned} \textrm{Uninfected cells} \qquad \dot{U} & = - bUV \\ \textrm{Infected cells} \qquad \dot{I} & = bUV - d_I I \\ \textrm{Dead cells} \qquad \dot{D} & = d_I I \\ \textrm{Virus} \qquad \dot{V} & = \frac{pI}{1+s_F F} - (d_V V + k^{'}_{A}A + b^{'} U)V\\ \textrm{Innate response} \qquad \dot{F} & = p_F - d_F F + \frac{g_F (F_{max} - F)V}{V+h_V} \\ \textrm{B cells} \qquad \dot{B} & = \frac{F V}{FV+h_F} g_B B \\ \textrm{Antibodies} \qquad \dot{A} & = r_A B - d_A A - k_{A}AV \\ \end{aligned} \]
Conceptual model suggests that protection (and morbidity) could be peaked.
See also: Rhodes et al 2016 Vaccine, Rhodes et al 2019 JTB
Data from a phase 2 clincial dose-finding study of a norovirus vaccine candidate. Work in progress.
For teaching (stable):
For research (WIP):
https://phdcomics.com/